Valve has explained why Steam installs DirectX every time you install a different game - even an old one from years ago.
It's not an error, nor is it to do with checking that your DirectX installation is up to date. Rather, it's to do with how Microsoft packages the software.
"Games which don't use the D3DX helpers (such as Source engine games) don't require running the annoying installer on first launch as they only depend on major D3D9/10/11 versions being installed. Howeer, games that do use D3DX must run it as it's the only way Microsoft has allowed for distributing and checking the version info on the files," explained Valve software engineer John McCaskey on the Steam forum.
"We can't stop. It's required due to a bad versioning/packaging scheme as well as bad redistribution licensing terms on the D3DX libraries."
"We can't stop. It's required due to a bad versioning/packaging scheme ...."
John McCaskey, Valve software engineer
"The one thing that could be made better on our side is that Steam could be smart enough to know if an exactly matching version of the DX installer is already downloaded and share that content so you don't download it with each game," he added.
"Since the installer is relatively small compared to most game installs that wouldn't be a huge win, though, and requires a good deal of new complexity for partners in how they package up their games and manage installation dependencies.
"You'd also still end up with lots of different versions of the installer, since as discussed above they are often targeting different D3DX versions and as such are all required. As such any improvement to avoid duplicates isn't an immediate priority, but we may be able to improve it slightly in the future."